Abstract

It is shown that the dipole moment function, $\mu$(R, Z$_a$, Z$_b$), for an arbitrary bound electronic state of a one-electron diatomic molecule, with inter-nuclear distance R and atomic numbers Z$_a$, Z$_b$ may be expressed exactly in terms of the separation eigenconstant C and the electronic energy eigenvalue W of the Schrodinger equation by means of the Hellmann-Feynman theorem and a new recursion relation. The formula is used to investigate the behaviour of $\mu$ in the vicinity of the united atom and when the nuclei are far apart. The generalization required to extend the relation to other expectation values is derived in an appendix.